5 papers
Compositional Information Geometry of Probabilistic Programs
Jacek Karwowski, Frank Nielsen, Sam Staton
We study the compositional, intensional information geometry of probabilistic programs. For a first-order probabilistic programming language with finite random variables, we constr…
pyBregMan: A Python library for Bregman Manifolds
Frank Nielsen, Alexander Soen
A Bregman manifold is a synonym for a dually flat space in information geometry which admits as a canonical divergence a Bregman divergence. Bregman manifolds are induced by smooth…
Tempered Calculus for ML: Application to Hyperbolic Model Embedding
Richard Nock, Ehsan Amid, Frank Nielsen +2
Most mathematical distortions used in ML are fundamentally integral in nature: -divergences, Bregman divergences, (regularized) optimal transport distances, integral probability…
The Tempered Hilbert Simplex Distance and Its Application To Non-linear Embeddings of TEMs
Ehsan Amid, Frank Nielsen, Richard Nock +1
Tempered Exponential Measures (TEMs) are a parametric generalization of the exponential family of distributions maximizing the tempered entropy function among positive measures sub…
Optimal Transport with Tempered Exponential Measures
Ehsan Amid, Frank Nielsen, Richard Nock +1
In the field of optimal transport, two prominent subfields face each other: (i) unregularized optimal transport, "à-la-Kantorovich", which leads to extremely sparse plans but with…